matita/matita/contribs/lambda_delta/basic_2/computation/ysteps.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/substitution/csup.ma".
  16 include "basic_2/computation/yprs.ma".
  17
  18 (* ITERATED STEP OF HYPER PARALLEL COMPUTATION ON CLOSURES ******************)
  19
  20 inductive ysteps (h) (g) (L1) (T1) (L2) (T2): Prop ≝
  21 | ysteps_intro: h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄ → (L1 = L2 → T1 = T2 → ⊥) →
  22                 ysteps h g L1 T1 L2 T2
  23 .
  24
  25 interpretation "iterated step of hyper parallel computation (closure)"
  26    'YPRedStepStar h g L1 T1 L2 T2 = (ysteps h g L1 T1 L2 T2).
  27
  28 (* Basic properties *********************************************************)
  29
  30 lemma ssta_ysteps: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l + 1] U →
  31                    h ⊢ ⦃L, T⦄ •⭃*[g] ⦃L, U⦄.
  32 #h #g #L #T #U #l #HTU
  33 @ysteps_intro /3 width=2/ #_ #H destruct
  34 elim (ssta_inv_refl … HTU)
  35 qed.
  36
  37 lemma csup_ysteps: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ →
  38                    h ⊢ ⦃L1, T1⦄ •⭃*[g] ⦃L2, T2⦄.
  39 #h #g #L1 #L2 #T1 #T2 #H
  40 lapply (csup_fwd_cw … H) #H1
  41 @ysteps_intro /3 width=1/ -H #H2 #H3 destruct
  42 elim (lt_refl_false … H1)
  43 qed.